Marketing Percolation

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass 1969). This mean field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al 2000) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.Comment: to appear in Physica

Studies of Optical and Electronic Properties of Nanoparticles for Solar Energy Conversion

The higher energy needs for today\u27s technological society requires sustainable and renewable energy source, such as solar energy. This study focuses on using semiconducting quantum dots and fluorescent dyes as light absorbers for solar energy conversion devices such as solar cells. Quantum dots are small nanocrystals (usually 2-10 nm in diameter) with tunable absorbing properties. The smaller the dot, the shorter the wavelength being absorbed. Quantum dots are extremely efficient light absorbers and emitters. Fluorescent dyes have a high quantum yield. In order to examine the energy conversion, cadmium selenide (CdSe) quantum dots and Rhodamine 6G (R6G) dye were spin coated onto graphene (two dimensional nanomaterial). The Kish graphene is mechanically exfoliated to produce graphene. The graphene is then placed onto SiO2/Si substrate. The number of graphene layers present was estimated through a fluorescence microscope. Lifetime measurements were carried out through time resolved photoluminescence. Trials were conducted with rhodamine 6G both with and without the presence of graphene flakes. Lifetime was found to decrease when rhodamine 6G was placed over the graphene flakes, which is indicative of energy transfer. Lifetime studies of cadmium selenide quantum dot films were also conducted. Tests will continue to determine the effects of cadmium selenide quantum dots placed on top of graphene. Comparisons and analyzation will between the lifetimes of these two materials on graphene will then be determined. These studies will contribute to the ongoing research towards the understanding of energy conversion

Energy Transfer in CdSe Nanoplatelet Superlattices

Two-dimension CdSe semiconductor nanoplatelets (NPLs) exhibit unique, highly desirable optical and electronic properties, such as large absorption crossection and bright emission. Fӧrster resonance energy transfer (FRET) between NPLs is responsible for the utility of these NPLs in fields such as lasing, lighting, solar energy, and sensing. Here we study energy transfer processes in NPL superlattices using photoluminescence (PL) and time resolved PL (TRPL) spectroscopic methods. Information on the effect of thickness of NPL is obtained through correlating PL and TRPL spectra of CdSe superlattices with AFM measurements. PL spectrum showed narrow fluorescence and absorption peaks at room temperature corresponding to excitonic transitions. A FRET lifetime of 351 ps was observed. Results suggest that FRET occurs more rapidly in CdSe NPL superlattices than in isolated CdSe NPLs and that FRET lifetimes depend on available energy pathways in the surrounding environment. This is a promising new material in the field of semiconductors and optical applications

Temperature-dependent Exciton Dynamics of Superacid Treatment in Monolayers of the Metal Dichalcogenide MoS2

To improve optoelectronic semiconductor materials, one of the most efficient research areas is the two-dimensional (2D) transition-metal dichalocogenides (TMDCs). It has been shown that organic nonoxidizing superacid bis(trifluoromethane)sulfonamide (TFSI) treatment of molybdenum disulfide (MoS2) monolayer could uniformly enhance its photoluminescence by more than two orders of magnitude and also extend the lifetime of excitons. This could greatly improve the efficiency of the solar energy usage, but the mechanism behind it has not been fully understood. Extreme low temperatures (approximately 7K), which slow the surface exciton mobility, were applied to investigate the changes of treated MoS2 monolayer surfaces. This approach also requires cover slip caps to protect samples from degrading in the vacuum and low temperature environment. Our results show that the defect stages of the MoS2 surface still occur at low temperatures which differs from the previous mechanism proposed. To determine the true mechanism of superacid treatment of MoS2 monolayer we will need further experiments

Superradiant and subradiant states in lifetime-limited organic molecules through laser-induced tuning

An array of radiatively coupled emitters is an exciting new platform for generating, storing, and manipulating quantum light. However, the simultaneous positioning and tuning of multiple lifetime-limited emitters into resonance remains a significant challenge. Here we report the creation of superradiant and subradiant entangled states in pairs of lifetime-limited and sub-wavelength spaced organic molecules by permanently shifting them into resonance with laser-induced tuning. The molecules are embedded as defects in an organic nanocrystal. The pump light redistributes charges in the nanocrystal and dramatically increases the likelihood of resonant molecules. The frequency spectra, lifetimes, and second-order correlation agree with a simple quantum model. This scalable tuning approach with organic molecules provides a pathway for observing collective quantum phenomena in sub-wavelength arrays of quantum emitters

Exciton level structure and dynamics in tubular porphyrin aggregates

We present an account of the optical properties of the Frenkel excitons in self-assembled porphyrin tubular aggregates that represent an analog to natural photosynthetic antennae. Using a combination of ultrafast optical spectroscopy and stochastic exciton modeling, we address both linear and nonlinear exciton absorption, relaxation pathways, and the role of disorder. The static disorder-dominated absorption and fluorescence line widths show little temperature dependence for the lowest excitons (Q band), which we successfully simulate using a model of exciton scattering on acoustic phonons in the host matrix. Temperature-dependent transient absorption of and fluorescence from the excitons in the tubular aggregates are marked by nonexponential decays with time scales ranging from a few picoseconds to a few nanoseconds, reflecting complex relaxation mechanisms. Combined experimental and theoretical investigations indicate that nonradiative pathways induced by traps and defects dominate the relaxation of excitons in the tubular aggregates. We model the pump?probe spectra and ascribe the excited-state absorption to transitions from one-exciton states to a manifold of mixed one- and two-exciton states. Our results demonstrate that while the delocalized Frenkel excitons (over 208 (1036) molecules for the optically dominant excitons in the Q (B) band) resulting from strong intermolecular coupling in these aggregates could potentially facilitate efficient energy transfer, fast relaxation due to defects and disorder probably present a major limitation for exciton transport over large distances. We present an account of the optical properties of the Frenkel excitons in self-assembled porphyrin tubular aggregates that represent an analog to natural photosynthetic antennae. Using a combination of ultrafast optical spectroscopy and stochastic exciton modeling, we address both linear and nonlinear exciton absorption, relaxation pathways, and the role of disorder. The static disorder-dominated absorption and fluorescence line widths show little temperature dependence for the lowest excitons (Q band), which we successfully simulate using a model of exciton scattering on acoustic phonons in the host matrix. Temperature-dependent transient absorption of and fluorescence from the excitons in the tubular aggregates are marked by nonexponential decays with time scales ranging from a few picoseconds to a few nanoseconds, reflecting complex relaxation mechanisms. Combined experimental and theoretical investigations indicate that nonradiative pathways induced by traps and defects dominate the relaxation of excitons in the tubular aggregates. We model the pump?probe spectra and ascribe the excited-state absorption to transitions from one-exciton states to a manifold of mixed one- and two-exciton states. Our results demonstrate that while the delocalized Frenkel excitons (over 208 (1036) molecules for the optically dominant excitons in the Q (B) band) resulting from strong intermolecular coupling in these aggregates could potentially facilitate efficient energy transfer, fast relaxation due to defects and disorder probably present a major limitation for exciton transport over large distances

Hyperspectral imaging of exciton confinement within a moiré unit cell with a subnanometer electron probe

Electronic and optical excitations in two-dimensional systems are distinctly sensitive to the presence of a moiré superlattice. We used cryogenic transmission electron microscopy and spectroscopy to simultaneously image the structural reconstruction and associated localization of the lowest-energy intralayer exciton in a rotationally aligned WS2-WSe2 moiré superlattice. In conjunction with optical spectroscopy and ab initio calculations, we determined that the exciton center-of-mass wave function is confined to a radius of approximately 2 nanometers around the highest-energy stacking site in the moiré unit cell. Our results provide direct evidence that atomic reconstructions lead to the strongly confining moiré potentials and that engineering strain at the nanoscale will enable new types of excitonic lattices

Holistic energy landscape management in 2D/3D heterojunction via molecular engineering for efficient perovskite solar cells

Constructing two-dimensional (2D) perovskite atop of 3D with energy landscape management is still a challenge in perovskite photovoltaics. Here, we report a strategy through designing a series of π-conjugated organic cations to construct stable 2D perovskites and to realize delicate energy level tunability at 2D/3D heterojunctions. As a result, the hole transfer energy barriers can be reduced both at heterojunctions and within 2D structures, and the preferable work function shift reduces charge accumulation at interface. Leveraging these insights and also benefitted from the superior interface contact between conjugated cations and poly(triarylamine) (PTAA) hole transporting layer, a solar cell with power conversion efficiency of 24.6% has been achieved, which is the highest among PTAA-based n-i-p devices to the best of our knowledge. The devices exhibit greatly enhanced stability and reproducibility. This approach is generic to several hole transporting materials, offering opportunities to realize high efficiency without using the unstable Spiro-OMeTAD